diff --git a/paper/paper.md b/paper/paper.md
index 80bb913..ad95d1a 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -117,15 +117,17 @@ The score-based diffusion model for the data is fit by optimising the parameters
 $$
     % \mathbb{E}_{t\sim\mathcal{U}(0, T)}\mathbb{E}_{\boldsymbol{x}\sim p(\boldsymbol{x})}[\lambda(t)||\nabla_{\boldsymbol{x}}\log p_t(\boldsymbol{x}) - \boldsymbol{s}_{\theta}(\boldsymbol{x},t)||_2^2]
 
-    \mathcal{L}(\theta) = \mathbb{E}_{t\sim\mathcal{U}(0, T)}\mathbb{E}_{\boldsymbol{x}\sim p(\boldsymbol{x})}\mathbb{E}_{\boldsymbol{x}(t)\sim p(\boldsymbol{x}(t)|\boldsymbol{x})}[\lambda(t)||\nabla_{\boldsymbol{x}}\log p_t(\boldsymbol{x}(t)|\boldsymbol{x}(0)) - \boldsymbol{s}_{\theta}(\boldsymbol{x}(t),t)||_2^2]
-
+    % \mathcal{L}(\theta) = \mathbb{E}_{t\sim\mathcal{U}(0, T)}\mathbb{E}_{\boldsymbol{x}\sim p(\boldsymbol{x})}\mathbb{E}_{\boldsymbol{x}(t)\sim p(\boldsymbol{x}(t)|\boldsymbol{x})}[\lambda(t)||\nabla_{\boldsymbol{x}}\log p_t(\boldsymbol{x}(t)|\boldsymbol{x}(0)) - \boldsymbol{s}_{\theta}(\boldsymbol{x}(t),t)||_2^2]
+    x
 $$
 
 where $\lambda(t)$ is an arbitrary scalar weighting function, chosen to preferentially weight certain times - usually near $t=0$ where the data has only a small amount of noise added. Here, $p_t(\boldsymbol{x}(t)|\boldsymbol{x}(0))$ is the transition kernel for Gaussian diffusion paths. This is defined depending on the form of the SDE [@sde] and for the common variance-preserving (VP) SDE the kernel is written as 
 
 $$
-    p(\boldsymbol{x}(t)|\boldsymbol{x}(0)) = \mathcal{G}[\boldsymbol{x}(t)|\mu_t \cdot \boldsymbol{x}(0), \sigma^2_t \cdot \mathbb{I}]
+    % p(\boldsymbol{x}(t)|\boldsymbol{x}(0)) = \mathcal{G}[\boldsymbol{x}(t)|\mu_t \cdot \boldsymbol{x}(0), \sigma^2_t \cdot \mathbb{I}]
+    x
 $$
+
 where $\mathcal{G}[\cdot]$ is a Gaussian distribution, $\mu_t=\exp(-\int_0^t\text{d}s \; \beta(s))$ and $\sigma^2_t = 1 - \mu_t$. $\beta(t)$ is typically chosen to be a simple linear function of $t$.
 
 In Figure \ref{fig:sde_ode} the forward and reverse diffusion processes are shown for a samples from a Gaussian mixture with their corresponding SDE and ODE paths.